Abstract

I find myself agreeing with much of the detail of the Jaffe-Quinn argument, especially the importance of distinguishing between results based on rigorous proofs and those which have a heuristic basis. Overall, however, I rebel against their general tone and attitude which appears too authoritarian. My fundamental objection is that Jaffe and Quinn present a sanitized view of mathematics which condemns the subject to an arthritic old age. They see an inexorable increase in standards of rigour and are embarrassed by earlier periods of sloppy reasoning. But if mathematics is to rejuvenate itself and break exciting new ground it will have to allow for the exploration of new ideas and techniques which, in their creative phase, are likely to be as dubious as in some of the great eras of the past. Perhaps we now have high standards of proof to aim at but, in the early stages of new developments, we must be prepared to act in more buccaneering style. The history of mathematics is full of instances of happy inspiration triumphing over a lack of rigour. Euler’s use of wildly divergent series or Ramanujan’s

Citations